
where \(\left|{\pm m} \right\rangle \)  refer to the photon states with OAMs of \( \pm m\hbar \)  per photon, respectively. The four OAM Bell states can also be divided into two categories of Boson states (\(\left|{\mu ^{\pm }} \right\rangle _{12}\)  and \(\left|{\nu ^{+}} \right\rangle _{12}\) ) and Fermion state (\(\left|{\nu ^{-}} \right\rangle _{12}\) ), leading to three central dips and one central peak in the HOM interference curves shown in Fig. REF (a). When exploring two-photon interference in two DoFs of polarization and OAM, a hyper-entangled state (Boson/Fermion-Boson/Fermion state) in the form of the product of a polarization Bell state and an OAM Bell state can be prepared for two photons, as shown in Fig. REF (b). Interesting conclusions would be expected for the two-photon interference with hyper-entangled state according to the general physics law that more is different [1]}.
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